Some comments:
1) Ad footnote 3: we do indeed learn it because we say that the number of inversions (which I give) is a lower bound. I elaborate a bit now.
2) "Adjecency list" denots only one list for one node, afaik; the set of lists is typically stored in an array, not a list.
3) The e_i that appear in the example of answer 2 are "defined" in the method section. Too subtle?